Efficient Bayesian multi-source localization using a graphics processing unit

This paper presents a highly-efficient approach to matched-field localization of an unknown number of ocean acoustic sources employing a graphics processing unit (GPU) for massively parallel computations. A Bayesian formulation is developed in which the number, locations, and complex spectra (amplitudes and phases) of multiple sources, as well as noise variance at each frequency, are considered unknown random variables constrained by acoustic data and prior information. The number of sources is determined during an initial burn-in stage by minimizing the Bayesian information criterion using an efficient birth/death scheme. Marginal posterior probability distributions for source locations are then computed using Gibbs sampling. Source and noise spectra are sampled implicitly by applying analytic maximum-likelihood solutions in terms of the source locations (explicit parameters). This greatly reduces the dimensionality of the inversion, but requires solving a very large number (order 105) of complex matrix inversions for each sample of the explicit parameters. These inversions can be solved in parallel on a GPU, increasing efficiency by a factor of ~100. Examples are given of localizing a large number of sources (up to 10) in near real time.